Green's formula with $\bbc^{*}$-action and Caldero-Keller's formula for cluster algebras
Quantum Algebra
2008-01-10 v2 Representation Theory
Abstract
It is known that Green's formula over finite fields gives rise to the comultiplications of Ringel-Hall algebras and quantum groups (see\cite{Green}, also see \cite{Lusztig}). In this paper, we deduce the projective version of Green's formula in a geometric way. Then following the method of Hubery in \cite{Hubery2005}, we apply this formula to proving Caldero-Keller's multiplication formula for acyclic cluster algebras of arbitrary type.
Keywords
Cite
@article{arxiv.0707.1175,
title = {Green's formula with $\bbc^{*}$-action and Caldero-Keller's formula for cluster algebras},
author = {Jie Xiao and Fan Xu},
journal= {arXiv preprint arXiv:0707.1175},
year = {2008}
}
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26 pages